Josh Jacobs is clearly VERY lucky to be alive today ... TMZ Sports has obtained the mug shot from just after the NFL star's car wreck this week -- and you can see he suffered a GNARLY head wound in the crash.
As we previously reported, cops say Jacobs wrecked his ride at round 4:42 AM near the Las Vegas airport on Monday.
And, in new police docs obtained by TMZ Sports, officers say Jacobs smelled like booze when they found him at the crash site.
In the docs, cops claim as Jacobs was explaining to them why he had crashed ... "a moderate odor of an unknown alcoholic beverage" was coming from the Raiders running back's mouth.
Cops say Jacobs was bleeding from a "large laceration" on his forehead as well ... and the officers added the 22-year-old told them he believed he had fallen asleep at the wheel just before the crash.
In the docs, officers say Jacobs was treated for his injuries and was transported to the hospital ... and once there, cops questioned him further about drinking and driving.
Cops say they performed a sobriety test on the NFL player while he was laying in his hospital bed ... but they say he passed that.
Still, officers in the docs claim he "did however have a strong odor of alcohol coming from his person."
Cops in the docs also say at some point during the morning Jacobs admitted to drinking before getting behind the wheel.
Cops claim they also reviewed surveillance video from the crash and believed they had enough to arrest Josh on suspicion of DUI.
For his part, Josh -- through his attorneys David Z. Chesnoff and Richard A. Schonfeld -- denied that he was drunk behind the wheel.
"We intend to enter a not guilty plea on behalf of Mr. Jacobs if he is ever charged," they said in a statement.